# Math Homework Help

### Showing All Questions Answered Popular Recommended Unanswered Editor's Choice in Math

• Math
Hello! Exponential growth function has a form `y=A*(1+r)^x,` where A is the initial value and r is the growth rate. If we substitute x=0 we obtain `y(0)=A*(1+r)^0=A.` Recall that y-intercept is the...

Asked by user7485737 on via web

• Math
The question is based on the similarity of triangles. In similar triangles ratio of the corresponding sides is same. So let's find the scale factor Scale factor=2/1.5 = 1.33 So,...

Asked by nivlac36 on via web

• Math
The y-intercept of a graph of the function is the y-coordinate of the point where the graph intersects y-axis. The x-coordinate of this point is 0. Therefore, to find the y-intercept, plug in x = 0...

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• Math
Hello! Let's denote the number of minivans washed as m and the number of cars as c. Then she earned 7m dollars for minivans and 4c for cars. It is given that `7m+4c=41.` If m and c could be...

Asked by emilys91612 on via web

• Math
t(1)=4 t(2)=4+4/5=24/5 t(3)=4+4/5+4/25=124/25 t(4)=4+4/5+4/25+4/125=624/125 For each nth term we take t(1) times r^(n-1): e.g. when n=4 we have 4(1/5)^3=4/125...

Asked by kerryannb2009 on via web

• Math
It depends on when you require the 10% return on your investment. If you require the 10% return in one year, then you will need to pay \$26.20. If you wanted to make 10% over 2 years, you would need...

Asked by user7182458 on via web

• Math
Hello! Actually, you cannot. Any rectangle has four sides, two pairs of which have equal length. If we denote the length of one side as x (inches), then one more side has the same length, and two...

Asked by jerameec on via web

• Math
Find c such that y=4x+2 is tangent to the curve `y=1/3 x^3+c ` The slope of the tangent line to a curve is given by the value of the first derivative. Since the line is tangent to the curve, we...

Asked by lilianm730 on via web

• Math
To solve, refer to the figure below. Let the length and width of the inscribed rectangle be l and w. So, its area is: `A = l * w` To express this as one variable, let's apply similar triangles....

Asked by annacpetty on via iOS

• Math
Hello! I think that i, j and k are mutually orthogonal unit vectors. In this case the length of a vector `x*i + y*j + z*k` is `sqrt(x^2+y^2+z^2).` So `|a| = sqrt(3^2+4^2+0^2) = sqrt(25) = 5,` `|b|...

Asked by user6896309 on via web

• Math
If you make a star with overlapping pieces this will create 10 triangles. There will be 5 on the outside and then 5 others on the inside. I've attached a document with the 5 on the inside shaded....

Asked by krishvjshah on via web

• Math
We'll use the formula `(a-b)*(a+b) = a^2-b^2.` Multiply equation by `(sin(x)+sin(y))*(cos(x)+cos(y))` (the product of the denominators): `(cos(x)+cos(y))*(cos(x)-cos(y))...

Asked by enotes on via web

• Math
Verify `sqrt((1+sin(theta))/(1-sin(theta)))=(1+sin(theta))/|cos(theta)|` Working from the left side, we show that it is equivalent to the right side: `sqrt((1+sin(theta))/(1-sin(theta)))`...

Asked by enotes on via web

• Math
By squaring both sides you are assuming that the equality is true, but this is what was to be established. Better is to multiply left side by sqrt(1-cos)/sqrt(1-cos) resulting in...

Asked by enotes on via web

• Math
`cos(pi/2-b)=sin(b)` for all b. So the initial identity is equivalent to `cos^2(b)+sin^2(b)=1,` which is true.

Asked by enotes on via web

• Math
First, `sec(y) = 1/cos(y)` and `cot(y) = cos(y)/sin(y).` Second, `cos(pi/2-y) = sin(y)` and `sin(pi/2-y) = cos(y).` Therefore `sec^2(y) - cot^2(pi/2-y) = 1/(cos^2(y)) - (sin^2(y))/(cos^2(y)) =`...

Asked by enotes on via web

• Math
Verify the identity: `sin(t)csc(pi/2-t)=tan(t)` Simplify the left side of the equation by using the cofunction identity csc((pi/2)-t)=sec(t). `sin(t)sec(t)=tan(t)` Simplify the left side of the...

Asked by enotes on via web

• Math
First, `sec(x) = 1/cos(x)` and `cot(x) = cos(x)/sin(x).` Second, `cos(pi/2-x) = sin(x)` and `sin(pi/2-x) = cos(x).` Therefore the left part is `1/(cos^2(pi/2-x)) - 1 = 1/(sin^2(x)) - 1 =...

Asked by enotes on via web

• Math
For both sides to have sense, x must be in [-1, 1]. For those x'es `sin^(-1)(x)` is the angle y in `[-pi/2, pi/2]` such that sin(y)=x. cos is nonnegative on `[-pi/2, pi/2],` so `cos(y) =...

Asked by enotes on via web

• Math
For both sides to have sense, x must be in [-1, 1]. For such x'es, `sin^(-1)(x)` is the angle y in `[-pi/2, pi/2]` such that `sin(y) = x.` But `cos^2(y) + sin^2(y) = 1,` so `cos^2(y) = 1 - sin^2(y)...

Asked by enotes on via web

• Math
For `sin^(-1)((x-1)/4)` to have sense, (x-1)/4 must be in [-1, 1]. In this case, `sin^(-1)((x-1)/4)` is an angle y in `[-pi/2, pi/2]` such that sin(y) = (x-1)/4. For those angles `cos(y) gt= 0`...

Asked by enotes on via web

• Math
You need to rremember that `tan^2 theta+ 1 = 1/(cos^2 theta)` , hence, replacing `cos^(-1) ((x+1)/2)` by `alpha` , yields: `cos^(-1) ((x+1)/2) = alpha => cos(cos^(-1) ((x+1)/2)) = cos alpha`...

Asked by enotes on via web

• Math
cot(x)=1/tan(x) and tan(x)=1/cot(x). So the left side is cot(x)+tan(x) and the right is tan(x)+cot(x), which are the same.

Asked by enotes on via web

• Math
Verify the identity: `1/sin(x)-1/csc(x)=csc(x)-sin(x)` Simplify the left side of the equation using the following reciprocal identities: 1/sin(x)=csc(x) and 1/csc(x)=sin(x)....

Asked by enotes on via web

• Math
Transform the left part: `(1 + sin(theta))/cos(theta) + cos(theta)/(1 + sin(theta)) =` `((1 + sin(theta))^2 + cos^2(theta))/(cos(theta)*(1 + sin(theta))) =` `(1 + 2sin(theta) + sin^2(theta) +...

Asked by enotes on via web

• Math
Verify the identity `cos(theta)cot(theta)/(1-sin(theta))-1=csc(theta)` `(cos(theta)cot(theta))/(1-sin(theta))-1=csc(theta)` Rewrite `cot(theta)` as a quotient....

Asked by enotes on via web

• Math
Verify the identity: `1/(cos(x)+1)+1/(cos(x)-1)=-2csc(x)cot(x)` `[cos(x)-1+cos(x)+1]/(cos^2(x)-1)=-2csc(x)cot(x)` `[2cos(x)]/(cos^2(x)-1)=-2csc(x)cot(x)` Use the pythagorean identity...

Asked by enotes on via web

• Math
Verify the identity. `cos(x)-[cos(x)/(1-tan(x))]=(sinxcosx)/(sinx-cosx)` `[cos(x)(1-tan(x))-cos(x)]/[1-tan(x)]=[sin(x)cos(x)]/[sin(x)-cos(x)]`...

Asked by enotes on via web

• Math
By definition, tan(t)=sin(t)/cos(t). Also, `sin(pi/2-t)=cos(t)` and `cos(pi/2-t)=sin(t).` Therefore `tan(pi/2-t)=cos(t)/sin(t)` and `tan(pi/2-t)*tan(t)=1,` QED.

Asked by enotes on via web

• Math
Verify the identity: `[cos[(pi/2)-x]]/[sin[(pi/2)-x]]=tanx` Simplify the left side of the equation using the cofunction identity. `sin(x)/cos(x)=tanx` Simplify the left side of the equation using...

Asked by enotes on via web

• Math
Verify the identity: `[tan(x)cot(x)]/cos(x)=sec(x)` Simplify the numerator on the left side of the equation. Since tan(x) and cot(x) are reciprocals their product is 1. `1/cos(x)=sec(x)` Simplify...

Asked by enotes on via web

• Math
Verify the identity: `csc(-x)/sec(-x)=-cot(x)` Simplify the left side of the equation using the following even/odd identities: csc(-x)=-csc(x) and sec(-x)=sec(x) `[-csc(x)]/sec(x)=-cot(x)`...

Asked by enotes on via web

• Math
Verify (1+sin(y))(1-sin(y))=cos^2(y): Working from the left side we show that it is equivalent to the right side: (1+sin(y))(1-sin(y)) =1-sin^2(y) =cos^2(y) using the pythagorean identity

Asked by enotes on via web

• Math
Verify the identity: `[tan(x)+tan(y)]/[1-tan(x)tan(y)]=[cot(x)+cot(y)]/[cot(x)cot(y)-1]` Divide every term on the left side of the equation by tan(x)tan(y)...

Asked by enotes on via web

• Math
Verify the identity: `[tan(x)+cot(y)]/[tan(x)cot(y)]=tan(y)+cot(x)` Rewrite the left side of the equation as two fractions. `tan(x)/[tan(x)cot(y)]+cot(y)/[tan(x)cot(y)]=tan(y)+cot(x)`...

Asked by enotes on via web

• Math
Verify `cos(x)+sin(x)tan(x)=sec(x)` : `cos(x)+sin(x)tan(x)` `=cos(x)+sin(x)*sin(x)/cos(x)` `=cos(x)+sin^2(x)/cos(x)` `=(cos^2(x)+sin^2(x))/cos(x)` `=1/cos(x)` `=sec(x)` as required.

Asked by enotes on via web

• Math
First, `(1-x)*(1+x)=1-x^2.` So the left part is `1-sin^2(alpha),` which is obviously equal to `cos^2(alpha).`

Asked by enotes on via web

• Math
Verify the identity: `cos^2(beta)-sin^2(beta)=2cos^2(beta)-1` Use the pythagorean identity `sin^2(beta)+cos^2(beta)=1.` If `sin^2(beta)` is isolated the pythagorean identity would be...

Asked by enotes on via web

• Math
Verify `cos^2(beta)-sin^2(beta)=1-2sin^2(beta)` Working from the left side, we show that it is equivalent to the right side: `cos^2(beta)-sin^2(beta)` `=(1-sin^2(beta))-sin^2(beta)`...

Asked by enotes on via web

• Math
Verify: `sin^2(alpha)-sin^4(alpha)=cos^2(alpha)-cos^4(alpha)` Use the pythagorean identity `sin^2(alpha)+cos^2(alpha)=1` if `sin^2(alpha)` is isolated the pythagorean identity is...

Asked by enotes on via web

• Math
L.H.S `(tan^2(theta))/sec(theta) = tan^2(theta)*cos(theta) = tan(theta)*cos(theta)*{tan(theta)} =` `tan(theta)*cos(theta)*{sin(theta)/cos(theta)} = tan(theta)*sin(theta) = ` R.H.S

Asked by enotes on via web

• Math
You need to remember that `1/(csc t) = sin t` , hence, replacing `sin t` for `1/(csc t)` to the left side, yields: `sin t*cot^3 t = (cos t)*(csc^2 t - 1)` You need to replace `(cos^3 t)/(sin^3 t) `...

Asked by enotes on via web

• Math
`cot(t) = cos(t)/sin(t),` `csc(t) = 1/sin(t).` So `(cot^2(t))/csc(t) = (cos^2(t))/(sin^2(t))*(1/(1/sin(t))) =(cos^2(t))/(sin^2(t))*sin(t) = (cos^2(t))/sin(t),` which is the same as the right part...

Asked by enotes on via web

• Math
Verify the identity: `1/tan(beta)+tan(beta)=[sec^2(beta)]/tan(beta)` `[1+tan^2(beta)]/tan(beta)=[sec^2(beta)]/tan(beta)` Use the pythagorean identity `1+tan^2(beta)=sec^2(beta).`...

Asked by enotes on via web

• Math
Verify the identity. `sin^(1/2)(x)cos(x)-sin^(5/2)(x)cos(x)=cos^3(x)sqrt(sin(x))` Factor out the GCF `sin^(1/2)(x)cos(x).` `sin^(1/2)(x)cos(x)[1-sin^2(x)]=cos^3(x)sqrt(sin(x))` Use the pythagorean...

Asked by enotes on via web

• Math
Verify the identity. `sec^6(x)(sec(x)tan(x))-sec^4(x)(sec(x)tan(x))=sec^5(x)tan^3(x)` Factor out the GCF `sec^4(x)(sec(x)tan(x))` `sec^4(x)(sec(x)tan(x))[sec^2(x)-1]=sec^5(x)tan^3(x)` Use the...

Asked by enotes on via web

• Math
Verify cot(x)/sec(x)=csc(x)-sin(x): Working from the left side, we show that it is equivalent to the right side: cot(x)/sec(x) `=((cos(x))/(sin(x)))/(1/(cos(x)))` `=(cos^2(x))/(sin(x))`...

Asked by enotes on via web

• Math
Verify the identity: `[sec(theta)-1]/[1-cos(theta)]=sec(theta)` Use the reciprocal identity `cos(theta)=1/sec(theta)` `[sec(theta)-1]/[1-cos(theta)]=sec(theta)`...

Asked by enotes on via web

• Math
Verify the identity: `sec(x)-cos(x)=sin(x)tan(x)` The reciprocal of sec(x)=1/cos(x). `sec(x)-cos(x)=sin(x)tan(x)` `1/cos(x)-cos(x)=sin(x)tan(x)` `[1-cos^2(x)]/cos(x)=sin(x)tan(x)` Use the...

Asked by enotes on via web