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3 years ago

A rectangle has a width represented by x and length represented by 4x. it the area of the rectangle is 80, find the value of x

Mathematics

1 answer:

Brut [27]3 years ago

3 0

Area = length * width = 4x * x = 4x^2.

4x^2 = 80
x^2 = 80/4 = 20

x = sqrt 20

Answer is 4.47 to nearest hundredth.

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krek1111 [17]

Answer:

86 cm²

Step-by-step explanation:

1) Calculate the area of the square

$A=lw\\A=20*20\\A=400$

Therefore, the area of the square is 400 cm².

2) Calculate the area of the circle

$A=\pi r^2\\$

$\pi$ we can substitute with 3.14. To find the radius, we divide the diameter of the circle by 2. 20 cm is the diameter of the circle, so therefore, its radius is 10 cm.

$A=3.14*10^2\\A=3.14*100\\A=314$

Therefore, the area of the circle is 314 cm².

3) Subtract the area of the circle from the area of the square

$A=400-314\\A=86$

Therefore, the area of the shaded region is 86 cm².

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s2008m [1.1K]

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3 years ago

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nekit [7.7K]

Answer:

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If log2 5 = k, determine an expression for log32 5 in terms of k.

lukranit [14]

Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

$2^5$

Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

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laila [671]

Answer: y= 2

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