1) 6^(3x)=104
loga =logarithm to the base a
loga n=z ⇔a^z=n
Therefore:
log6 104=3x
x=(log6 104) / 3
x=(ln 104) / 3ln 6=0.8640279....≈0.864 (loga z=ln a / ln z)
Answer: x≈0.864
2) log3 (x+2)+ log3 (4x-1)=5
log3 x=5 ⇔ 3⁵=x ⇒x=243
log3 [(x+2)(4x-1)]=log3 243
log3 (4x²+7x-2)=log3 243
Therefore:
4x²+7x-2=243
4x²+7x-245=0
we solve this square equation:
x=[-7⁺₋√(49+3920)] / 8 =(-7⁺₋63) / 8
we have two solutions:
x₁=(-7-63) / 8=-8.75 this solution is not valid.
x₂=(-7+63) /8=7
Answer: x=7
Answer:
The rectangle is 8 ft by 6 ft.
Step-by-step explanation:
Let x = length and y = width
Then, 2x+2y = 28 and xy = 48
Since 2x+2y = 28, y = 14 - x
So, x(14 - x) = 48
x2 - 14x + 48 = 0
(x-8)(x-6) = 0
x = 8 or x = 6
Hope this helps!
Explanation:
The function is
To plot the function in the graph, first we shall determine the amplitude, period, phase shift and vertical shift.
The function is of the form,
where A is the amplitude =
Period is ,
Phase shift is C,
Vertical shift is D.
Hence, from the function , we have,
Amplitude =
Period =
Phase shift = 0
Vertical shift = -2
Now, substituting the values for x, we get the corresponding values for y.
For ⇒
For ⇒
For ⇒
For ⇒
For ⇒
Hence, plotting these points we get the graph which is attached below:
Now, we shall graph the function
Similarly, we shall determine the amplitude, period, phase shift and vertical shift.
Amplitude =
Period =
Phase shift = 0
Vertical shift = 1
Now, substituting the values for x, we get the corresponding values for y in the function
For ⇒
For ⇒
For ⇒
For ⇒
For ⇒
Hence, plotting these points we get the graph which is attached below:
Answer:
Perimeter: 36 m
Area: 60 m squared
Step-by-step explanation:
The perimeter is the sum of the exterior side lengths of the shape. Here, we see that there are two side lengths given, but we need to find the third one.
Notice that the triangle is split up into two right triangles, which means that we can use the Pythagorean Theorem to solve for half of the remaining side. The right triangles have hypotenuses of 13 and one leg of 12. That means the second leg will be .
So, the third side is made up of the two legs with length 5. This makes the length of the remaining side: 5 + 5 = 10.
Now, we can calculate the perimeter: P = 10 + 13 + 13 = 36 meters.
The area is calculated by the formula: , where b is the base and h is the height. Here, the base is what we found above, 10, and the height is the length that makes a perpendicular with the base, which is 12. So, the area is: . So, the area is 60 square meters.
Hope this helps!